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We present a scheme to entangle two microwave fields by using the nonlinearmagnetostrictive interaction in a ferrimagnet. The magnetostrictive interactionenables the coupling between a magnon mode (spin wave) and a mechanical mode inthe ferrimagnet, and the magnon mode simultaneously couples to two microwavecavity fields via the magnetic dipole interaction. The magnon-phonon couplingis enhanced by directly driving the ferrimagnet with a strong red-detunedmicrowave field, and the driving photons are scattered onto two sidebandsinduced by the mechanical motion. We show that two cavity fields can beprepared in a stationary entangled state if they are respectively resonant withtwo mechanical sidebands. The present scheme illustrates a new mechanism forcreating entangled states of optical fields, and enables potential applicationsin quantum information science and quantum tasks that require entangledmicrowave fields.

Magnetostrictively induced stationary entanglement between two microwave fields